document.write( "Question 1117777: What is the equation of the parabola with vertex (2 4) and focus (5 4)?\r
\n" ); document.write( "\n" ); document.write( "A) $\"y=%281%2F3%29+%28x-4%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "B) $\"y=%281%2F12%29+%28x-4%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "C) $\"x=%281%2F3%29+%28y-4%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "D) $\"x=%281%2F12%29+%28y-4%29%5E2%2B2\"$ \n" ); document.write( "

Algebra.Com's Answer #732902 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The focus is to the right of the vertex, so the parabola opens to the right; x is the dependent variable. So the answer is either C or D.

\n" ); document.write( "(Note also that choices A and B not only define parabolas that open upward instead of to the right; but they also define parabolas with vertex (2,4) instead of (4,2).)

\n" ); document.write( "The general equation of a parabola like that is

\n" ); document.write( " $\"x-h+=+%281%2F%284p%29%29%28y-k%29%5E2\"$

\n" ); document.write( "where (h,k) is the vertex and p is the directed distance from the vertex to the focus.

\n" ); document.write( "In your example, the directed distance from the vertex to the focus, p, is 3, so 1/4p is 1/12 -- so answer D. \n" ); document.write( "

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